[Martin Taylor 950220 13:30]
Bill Leach 950219.02:14 EST
just checking to see if Martin is 'listening'
The Test in action, eh? Any mention of information theory is assumed to
be a disturbance to some perception of mine that I am controlling? I think
your Test needs to be a bit more subtle. It's a bit like Rick's testing
whether the inverted T control is for x-y or for x/y. Either comes close,
because they are highly correlated, but one is a lot closer than the other.
I think it is not "mention" of information theory that is the disturbance,
but misrepresentation of it. You haven't misrepresented it, so far as I
am aware.
In past discussions, I have taken the position that it is wrong to say
information theory is inapplicable. The interesting question is whether
application is useful, and to that question I have an open mind. I tend
to believe it may be, and Rick's latest message may provide a route toward
an answer. The problem has been that (as I have throughout argued) in a
single-loop control system, especially a linear one, there are much better
analytic tools, and information theory is unlikely to tell you anything
you didn't know already. But it might, and here's a possible approach:
Rick Marken (950217.1100)
maybe we can make this discussion of
information substantive if you would suggest one simple test that would put
information theory on the line? Does information theory make some
quantitative prediction about the behavior of a subject in a simple tracking
task-- a prediction that can be tested against data? Can you describe an
experiment I can do to test a QUANTITATIVE predciction of information theory?
Perhaps a prediction regarding the effects of disturbance bandwidth on some
parameter of tracking performance?
I've been puzzling about this for a couple of hours, and it seems to me that
there are a couple of places where one might look. As experimenters, we
have no direct influence on the subject's perceptual functions as such; we
can influence only three paths related to the disturbed loop (1) the
environmental feedback path, (2) the path between CEV and sensor, and (3)
the path between disturbing variable and CEV. Of these, both (2) and (3) are
open to criticism on the ground that the CEV is precisely a representation
of the transformation applied by the perceptual input function; any
change we impose in path (2) alters the actual thing that is controlled,
and any change we impose in path (3) is simply irrelevant. (I disagree
about path 2, but it is a probable criticism that should be avoided if
possible). This leaves effects within path 1.
In path 1 (output-to-CEV) there are two aspects we could alter: the time
lag between the human muscular output and the effect on the sensors, and
the consistency of the relationship. Both should alter the bandwidth of
controllable disturbance. In respect of the time delay, the effect is
directly computable by normal linear methods, and an informational analysis
should not be expected to give any different answer--in fact one should
expect the answer to be less precise, since it makes fewer assumptions
about the form of the feedback function.
That leaves variation in the feedback function as the only place where one
could plausibly make changes that should affect the bandwidth of control.
I would have to look at it more closely to make any quantitative prediction.
Qualitatively, it would seem that the information rate of the variation
in the feedback function should subtract from the information rate of the
controllable disturbance, but whether this subtraction is direct or whether
a gain factor shows up, I don't know.
···
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Back to Bill Leach:
PCT's insistance
that we control perceptions against disturbance **ALL DISTURBANCE** is
saying something very significant about everything that we believe.
PCT doesn't say this. It says that the few perceptions we control, at any
moment, are controlled against anything that affects those perceptions.
The ECU that controls a perception knows nothing about what causes any
change in that perception, so to that degree it is correct to refer to
"all disturbance" to THAT perception. But for almost all of our perceptions,
at any moment, we are not controlling against any disturbance. Some changes
in perceptions we "observe with interest," some we are not conscious of,
and some we control against.
As best as we our able to determine using our
science, it is the masses and forces that CAUSE the observed behaviour of
the "bouncy" ball. Accurate measurement of the factors that physics
theory tells us are relevent allow accurate prediction of the balls
behaviour. The "bounciness" of the ball does not.
But for other purposes, if you know the bounciness of the ball, that may
be enough--for instance, to know whether to use it in your tennis game.
Just as within the perceptual control hierarchy, higher-level perceptions
are built from lower-level perceptions, so the perception of "bounciness"
may be a perfectly legitimate and useful basis for other perceptions. One
doesn't have to go back to raw sensation for everything.
debating endlessly the bounciness of the ball only
serves to distract from understanding what is actually happening.
And debating endlessly how the ball comes to be bouncy means that someone
else wants the court before you start to play your tennis game. At the
same time, measuring the bounciness may allow you to start a pleasurable
game, whereas not measuring it may result in a game you both hate. It all
depends on which perceptions that you are interesting in controlling at that
moment.
===================
To answer a comment in another posting--I've never taken too much pleasure
in providing disturbances, as such,or in participating in conflicts. But
I must confess that I sometimes make statements that have the intention of
getting a rise out of Rick--as I suspect he does with me. If you perceive
me as making flat statements of fact with the intention of generating
disturbances other than to Rick, either I'm acting in ways I'm not perceiving,
or you aren't reading the levels of assertion that I try to keep straight.
Do you remember a few postings in which I said something along the lines
of "and that's a fact:-)" with or without smiley?
I don't quite go along with Niels Bohr, but he was on the right track
when he said: "Take everything I say as a question." Or words to that
effect, probably in Danish.
Martin